cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A243867 Sum of the numbers N*(n) and N**(n) in A242974.

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%I A243867 #23 Jun 23 2015 22:57:10
%S A243867 1,7,97,1289,20611,365775,7813466,212149365
%N A243867 Sum of the numbers N*(n) and N**(n) in A242974.
%H A243867 V. Shevelev, <a href="http://arXiv.org/abs/0912.4006">Theorems on twin primes-dual case</a>, arXiv:0912.4006 (Sections 10,14)
%F A243867 Let B(n) be the number of twin primes pairs not exceeding the n-th primorial M_n = A002110(n). Then we know that B(n) = O(M_n/(log(M_n))^2) = o(M_n/log((p_(n-1)))^2. For sufficiently large n, a(n) + B(n) >= 0.416...*M_n/(log(prime(n-1)))^2 (cf. Shevelev link) and thus for large n, for example, we have a(n) >= 0.4*M_n/(log(prime(n-1)))^2.
%Y A243867 Cf. A242974, A242719, A242720, A242758, A243803, A243804.
%K A243867 nonn,more
%O A243867 3,2
%A A243867 _Vladimir Shevelev_, Jun 13 2014
%E A243867 More terms from _Peter J. C. Moses_, Jun 13 2014